Economists expect the U.S. to face another recession in the next four years. After all, the current expansion is already more than seven years old, and since World War II the average period of economic growth has lasted slightly less than six years. The longest period of growth on record was 10 years.

Yet a piece of research from the Federal Reserve Bank of San Francisco (highlighted recently by the New York Times) concluded, convincingly, that economic expansions do not die of old age—an old expansion like our current one is not likelier to enter a recession in the next year than a young expansion.

So that means a recession isn’t likely within the next four years? Not so fast. The reason has to do with one of those pesky probability questions, the stuff of high school anxiety dreams.

We’ll explain: The San Francisco Fed used the same techniques that are used to study human mortality. Less than 1% of 50-year-old Americans will die in the next year. But as people age, these odds gradually climb. At age 60, there is slightly more than a 1% of dying in the next year. By age 70, it’s around 2%. By age 100, it’s a 35% chance, and so on.

The San Francisco Fed found this pattern doesn’t seem to be true of recessions. An expansion, they found, has about the same odds of ending no matter how old it is. (Please note that this research is focused only on an expansion’s length, and is in no way a claim that the expansion has been strong.)

Recessions, the San Francisco Fed found, are kind of like flipping a coin or rolling a die. Every time you flip a coin, the odds of heads are 50% and the odds of tails are 50%. Every time you roll a die, there’s a one-in-six chance you’ll roll a three. No matter how many times you’ve rolled or flipped, the odds of the next toss never change.

But what are the odds of flipping a coin four times and never getting heads? What are the odds of getting T-T-T-T? It’s only about 6%. (Each flip is 0.5 so the odds of four tails in a row is 0.5*0.5*0.5*0.5 = 0.0625.) You have about a 94% chance of flipping at least one head.

How about with dice? What are the odds of rolling the die four times and never getting a three? The odds of a three are one-in-six (17%). The odds of something other than a three are 83%. Your chance of having neither roll be a three, after two tosses is 69% (.83*.83). After three tosses, the odds are 57% (.83*.83*.83). After four tosses, the odds of having not rolled a three is just 48%. Each individual roll has the exact same odds, but the longer you play the game, the likelier you become to have a loss (this, ultimately, is why the house always wins).

These same principles of probability hold for recessions. The San Francisco Fed says the odds do not get worse from one year to the next. It’s always around a 23% chance of recession and a 77% chance of continued expansion. Each year is like a new roll of the die. That means, with San Francisco’s figures, that after two games of recession roulette, there’s only a 59% chance you will avoid recession (.77*.77). After three years, it’s a 46% chance of avoiding recession. After four years, the San Francisco Fed’s odds would imply only a 35% chance of having avoided a recession in all four years.

Economists in The Wall Street Journal’s monthly survey aren’t being more pessimistic than this. In fact, their median estimate is somewhat less worried than purely playing the probabilities.

Some people hate the whole process of estimating recession odds, since turning points in the past have been missed. That’s folly. The hope is that economists will eventually refine their techniques for determining when the economy is at risk of recession, so that policy makers, businesses and individuals can anticipate or even prevent it. But that requires continuing to estimate these risks, rather than giving up on the forecasting game altogether.

If the odds don’t change, the economy is like the craps player who won his last seven bets. He might be feeling hot and, hey, the odds of each individual roll never change. Craps games don’t die of old age. But nobody has bankrupted Las Vegas yet.

Cool insight, however I was hoping to learn about how SF conducted the study. It seems like the article starts out asserting its conclusion--that the probability model of a recession any given year is similar to an independent draw (coin flip, gamble, etc...). Why is this? The content only elaborates on the consequences of such an assumption, but that's just arithmetic.

Superficially, there do not appear to by any major imbalances which could lead to a recession in the US. However, there are quite a few imbalances overseas, and a lot of political risk and geopolitical risk in many places, including involving the US. Recession can occur when investors or consumers or businesses lose confidence as a result of some sort of disquieting, even alarming event or trend. There are a lot of signs, or signs of potential for those events or trends already, and there could be some that are entirely unexpected.